Do you have a splitter for the dvi/hdmi or do you plug them right in your computer?
If you plug them both in the computer it sounds like you need to start up with the hdmi cable only. Then plug in the DVI.
Then you will need to see if the hdmi stays as monitor 1. (screen resolution and then identify)
Switch the setting so that the dvi turns to monitor 1 and then switch it back again.restart the computer and see if it sticks like that.
Also what Operating System do you have? and what kind of monitor? on most monitors you can set up the starting mode (auto,hdmi,vga,displayport).
To summarize it sounds like the issue is the sequence of your screen. and with sequence i mean the order of the screen.